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Arizona lawmakers say their new immigration enforcement law will help them fight an illegal immigrant crime wave that is sweeping the state, a claim that is backed by studies and statistics that suggest border states have a disproportionately high number of criminals who are illegal immigrants.

"We've been inundated with criminal activity. It's just -- it's been outrageous," Arizona Gov. Jan Brewer told Fox News.

"Crime is off the chart in this state," added Pinal County Sheriff Paul Babeu, president of the Arizona Association of Sheriffs.

Critics have called Arizona officials racist, intolerant and downright unconstitutional for passing the law, which makes illegal immigration a state crime and allows police to demand documentation from anyone they suspect is an illegal immigrant.

While the correlation between illegal immigrants and crime is almost impossible to quantify precisely, the available numbers indicate that Arizona -- as well as California and Texas -- are dealing with increased crime as a result of high illegal immigrant populations and activity.

Part of this is because some of those immigrants are being arrested based on immigration-related charges. A Pew Hispanic Center report last year said "increased enforcement" of immigration laws accounts for part of the trend.

But there are other crimes, many of which are drug-related. Furthermore, illegal immigrants and smuggling organizations have been linked to some specific violent crimes in Arizona. Local officials frequently cite the rash of kidnappings in their state in defending the new law. The Department of Justice's latest National Drug Threat Assessment says there were 267 kidnappings in Phoenix last year and 299 in 2008. The report said the victims usually have a connection to immigrant smuggling groups or drug traffickers.

The report also showed that assaults against U.S. law enforcement on the southwestern border are on the rise. The report found that the number of attacks on Border Patrol agents increased 46 percent to 1,097 incidents in fiscal 2008. The report said the assaults were mostly related to immigrant smuggling.

Together, Arizona, California and Texas are now home to 4.7 million of the 11 million illegal immigrants the Department of Homeland Security estimates are in the country.

Other states with high illegal immigrant populations -- like Illinois -- do not have a lot of illegal immigrant prisoners. Federal statistics show the illegal immigrant population is actually underrepresented in Illinois prisons.

But a comprehensive study released late last year from the Center for Immigration Studies cited federal law enforcement data showing that illegal immigrants made up a disproportionate share of the state prison populations in California and Arizona.

In 2004, the year when the data was most recently available, 12.4 percent of California prisoners were illegal immigrants, as compared with an estimated 6.9 percent of the state population. In Arizona, 11.1 percent of the prison population was undocumented, compared with 7 percent of the overall state population. In Texas, the percentage was also slightly higher in the prisons than it was statewide.

A Government Accountability Office study from 2005 also found that most illegal immigrant arrests were happening in California, Texas and Arizona. The study sampled a prison population of more than 55,000 illegal immigrants, and found that 80 percent of all the arrests were in those three states.

But overall, it's hard to say that illegal immigrants have triggered a crime explosion in any of these states, though the recent killing of Arizona rancher Robert Krentz by a suspected illegal immigrant has served as a rallying cry for advocates of tougher enforcement.

FBI statistics show California and Texas had a violent crime average slightly higher than the national average 2008, while Arizona's average was slightly lower.

Jessica Vaughan, a co-author of the Center for Immigration Studies report and policy director at the think tank, said the bottom line is that connections between illegal immigrants and crime are hard to draw.

"We didn't find any evidence to support the idea that either immigrants are more prone to crime or less prone to crime than ... legally resident Americans," she said. "It's very tricky."

Vaughan said part of the problem is that no federal database keeps a dependable count of how many illegal immigrants are convicted of crimes. Federal prison data, for instance, breaks out non-citizens in its data, but that covers several groups and not just illegal immigrants.

Some jurisdictions do keep track, though, and with the data that is available, Vaughan said it's apparent that there is a connection between illegal immigrants and certain types of crimes, like drug trafficking and identify theft. And, she said, illegal immigrants have a tendency toward recidivism.

The GAO report found that of the undocumented residents surveyed, almost all of them had more than one arrest. They averaged about eight arrests per person. Nearly half of the offenses were for drug crimes or immigration violations.

But for those immigrants who are being caught and convicted, their immigration status itself is often the offense.

The Pew Hispanic Center study from February 2009 found that even though Hispanics make up 13 percent of the adult population, they accounted for 40 percent of sentenced federal offenders in 2007. Almost half of those offenses were immigration-related.